The 72 Indonesians and their supporters, led by the Rev. Seth Kaper-Dale, had appealed for the arrangement in the hope that with extra time, they would be able to figure out a way to secure permanent legal status, either though the courts or with the passage of immigration reform legislation in Washington.

Immigrant advocates had hoped the deal signaled a broader use of humanitarian release for illegal immigrants without criminal records and with deep ties to the community.

Now, though, the reprieve for the Indonesians is ending.

In recent weeks, most of the Indonesians, many of whom fled persecution of Christians inIndonesia years ago, have received letters from the Department of Homeland Securityordering them to appear at the agency’s Newark office, a one-way ticket to Indonesia in hand.

Their advocates have leapt into action, appealing to immigration officials for continued lenience and lobbying members of the state’s Legislature and Congressional delegation to intervene.

On Wednesday, Representatives Carolyn B. Maloney of New York and Frank Pallone Jr. of New Jersey, both Democrats, plan to submit a bill that would provide relief to many of the Indonesians. The bill would allow certain Indonesians who fled persecution in their homeland between 1997 and 2002 to resubmit asylum claims that had been denied because they missed a one-year filing deadline.

“It feels so un-American to not make room to keep families together, especially when folks came out of a time and place where there was tremendous violence,” Mr. Kaper-Dale said in a telephone interview on Tuesday as he led a 24-hour vigil and fast at his parish, the Reformed Church of Highland Park, N.J., in support of the Indonesians.

The advocates said the decision to end the so-called orders of supervision was surprising in light of recent assurances by the Obama administration that it would focus its enforcement strategy on illegal immigrants with criminal records, while sparing those with strong ties to the community and no criminal record.

In June, senior officials at the Homeland Security Department announced a policy to encourage immigration agents and lawyers to use prosecutorial discretion when deciding whether to pursue deportation. The policy expanded the factors immigration authorities can take into account in such decisions, including how long an illegal immigrant has been in the United States and whether the immigrant was brought to the country as a child. In addition, the directive gave federal immigration lawyers the authority to dismiss deportation proceedings against immigrants without serious criminal records.

Last month, Homeland Security officials, seeking to speed deportation of convicted criminals, said they would begin a review of all deportation cases in the immigration courts and begin training enforcement agents and government lawyers in the application of the new prosecutorial discretion guidelines.

Mr. Kaper-Dale said all the Indonesians he had been helping would seem to be worthy candidates for this sort of relief. Most have been in the country for at least a decade and have American-born children, steady jobs and no criminal records, he said.

Most of the Indonesians have filed requests for prosecutorial discretion, he said. “If these folks were good enough for discretion two years ago, why aren’t they good enough for discretion now?” the pastor asked.

Officials at Immigration and Customs Enforcement, an arm of Homeland Security, would not explain on Tuesday why the orders of supervision were ending now. In response to media inquiries, an agency spokesman issued a statement saying that the agency was reviewing appeals “on a case-by-case basis.”

The orders of supervision allowed “individuals to remain in the community — as opposed to in detention — while they pursue legitimate forms of immigration relief,” the statement said.

On Tuesday, however, 12 of the Indonesians, responding to an immigration agency order, appeared at the Newark office. They ignored demands that they bring plane tickets, Mr. Kaper-Dale said. Agency officials told them to return later this month and added that the agency would issue them plane tickets, the pastor said.

Among them was Grace Laloan, 42, who arrived in the United States in 2002 with her husband. She said the couple, both Christians of Chinese descent, had fled religious and ethnic persecution by the Muslim majority. They have an American-born daughter, now 7, and work in factories, Ms. Laloan said.

Officials told her they would inform her of her fate on Dec. 21. “I don’t know, maybe they’re going to send me back,” Ms. Laloan said. “It feels bad because I want to stay here.”

Under the terms of the bill proposed by Representatives Maloney and Pallone, an applicant must be an Indonesian citizen; must have entered the United States after Jan. 1, 1997, and before Nov. 30, 2002; must have had an asylum application rejected because of a late filing; and must not have a criminal record or be otherwise barred from receiving asylum, among other conditions.

Mr. Kaper-Dale said more than 1,000 Indonesians might be affected by the bill, including clusters in New York and New Hampshire for whom he helped secure orders of supervision in 2010.

“It is our hope through a pending Congressional action, I.C.E. will stay deportation proceedings,” Representative Maloney said in a statement.